Answer:
Step-by-step explanation:
12 14 33 35========1,234,000,124,581.
You pick a card at random. Without putting the first card back, you pick a second card at random.
6,7,8,9
What is the probability of picking a 6 and then picking a 9?
(Write you answer as a fraction or whole number)
NEED ASAP PLS!!!!!
Answer:
1/12 is the correct answer
Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected over the x-
axis. The reflected figure is labeled figure C. Which best explains why figure A is congruent to figure C?
4
3
1
3-2-11
99 +4
1 234
4
A
$65
A B and B C
A A, B B, C C
Fach trianola ie a rinht triannla
The reason why Figure A is congruent to Figure C is that they undergo the same sequence of transformations: a translation followed by a reflection.
The statement "Figure A is translated 3 units right and 2 units up. The translated figure is labeled Figure B. Figure B is reflected over the x-axis. The reflected figure is labeled Figure C" describes a sequence of transformations applied to Figure A to obtain Figure C.
When Figure A is translated 3 units right and 2 units up, it undergoes a rigid transformation known as a translation. This transformation preserves the shape and size of the figure. The translated figure, Figure B, will have the same dimensions and orientation as Figure A but will be shifted to the right and up.
When Figure B is reflected over the x-axis, it undergoes a reflection. This transformation flips the figure vertically, changing the sign of the y-coordinates of its vertices while keeping the x-coordinates the same. The reflected figure, Figure C, will have the same shape and size as Figure B, but it will be oriented in the opposite direction.
Since translations and reflections are both rigid transformations, they preserve congruence. Therefore, Figure A and Figure C are congruent because they undergo the same sequence of transformations (translation followed by reflection) from Figure A.
In conclusion, Figures A and C go through the same set of transformations, a translation and a reflection, which explains why they are congruent.
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Cameron sorts 56 books into groups of 5, but has some books left over
How many books are left over?
Cameron has 1 book left over after sorting it into group of 5
To determine the number of book left,
we need to first divide 56 by 5 [56 ÷ 5]
Quotient = 11
then find the remainder which is 1
therefore there os only 1 book left over
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What is the probability that you will be in district 12 with Katniss & Peeta?
Answer:
0
Step-by-step explanation:
theres only 2 people each district
Paxton invests $4850 at 7.6%/a simple interest. If she wants the money to increase to $8000, how long will she need to invest her money?
Therefore, Paxton will need to invest her money for approximately 21.62 years to increase her investment from $4850 to $8000 at a simple interest rate of 7.6% per year.
To determine how long Paxton needs to invest her money in order for it to increase to $8000, we can use the formula for simple interest:
I = P * r * t
Where:
I = Interest earned
P = Principal (initial investment)
r = Interest rate per year (expressed as a decimal)
t = Time (in years)
Given that Paxton invests $4850 at an interest rate of 7.6% per year, we have:
4850 * 0.076 * t = 8000
Simplifying the equation:
369.8t = 8000
To find t, we divide both sides of the equation by 369.8:
t ≈ 8000 / 369.8 ≈ 21.62 years
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Landon finds some dimes and quarters under the couch cushions. How many coins does he have if he has 5 dimes and 10 quarters? How many coins does he have if he has d dimes and q quarters?
Answer:
15 coins, d + q coins
Step-by-step explanation:
If asking for the amount (in $)
5(.10) + 10(.25) = 2.5+.5 = $3
He would have 0.1d + 0.25q for d dimes and q quarters.
Answer if the following statement is true of false. *
1.X=X?
True
O False
The statement is:
O True
Work/explanation:
The following statement is true, because 1x is indeed the same thing as x. So when combining like terms, 2x + x is the same thing as 2x + 1x, which evaluates to 3x.
Therefore this is the answer.What is (-,-) quadrant
In the context of a Cartesian coordinate system, the term "(-,-) quadrant" refers to the third quadrant, also known as Quadrant III.
The Cartesian coordinate system consists of four quadrants, numbered from I to IV in a counterclockwise direction. Each quadrant is defined by the signs of the x and y coordinates.
In Quadrant III, the x-coordinates are negative (represented by the "-") and the y-coordinates are also negative. This means that any point located in this quadrant will have both x and y values that are less than zero.
Visually, Quadrant III is situated below the x-axis and to the left of the y-axis. It is characterized by its lower left position in the coordinate plane.
Points in Quadrant III can be thought of as having a negative horizontal position (to the left of the origin) and a negative vertical position (below the origin).
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If the base of a square building and an equilateral triangle building have the same perimeter, how do the areas of their floors compare?
Answer:
let, perimeter of square = 4a
where a = side of square
let, perimeter of the equilateral triangle = 3b
where b= side of triangle
therfore, 4a=3b
a/b = 3/4
area of the square = [tex]a^{2}[/tex]
are of the triangle = [tex]\frac{\sqrt{3} }{4} b^{2}[/tex]
dividing both the areas we get,
[tex]\frac{a^{2} }{\frac{\sqrt{3} }{4}b^{2} }[/tex]
[tex]a^{2}*\frac{4}{\sqrt{3} b^{2}}[/tex]
[tex]\frac{a^{2} }{b^{2} } * \frac{4}{\sqrt{3} }[/tex]
[tex]\frac{3^{2} }{4^{2} } * \frac{4}{\sqrt{3} }[/tex]
[tex]\frac{3\sqrt{3} }{4}[/tex]
hope you understand
Step-by-step explanation:
Scores on the Wechsler Adult Intelligence Scale for the 20 to 34 age group are approximately Normally distributed with mean 110 and standard deviation 15. How high must a person score to be in the top 4% of all scores? (Round your answer to the nearest whole number, if necessary.)
Answer:
The person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.
Step-by-step explanation:
What is defined as the normal distribution?
A normal distribution is a data set arrangement in which the majority of values cluster inside the center of the range and the remainder taper off symmetrically toward any extreme.
A histogram inside a normal distribution curve is sometimes used to design the curve.
The formula for the normal distribution is;
z = (x - μ)/σ
where,
z = z- score, taken fro table
Mean μ = 110
Standard deviation σ = 15
Sample mean x.
If we want to be in the top 5%, we must outperform 95% of the remaining scores. So we must investigate.
In with us standard normal probability table, look up 0.95 and get the Z score that corresponds to that.
z = 1.7
Put the value in formula ad find x.
1. 7 = (x - 110)/15
x = 25.5 + 110
x = 135.5
x = 136 (whole number)
Thus, the person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.
In rectangle ABCD, AB = x, BC =x + 2, and AC = x +4. Find the value of x.
Answer:
x = 6
Step-by-step explanation:
the diagonal AC divides the rectangle into 2 right triangles.
Consider the right triangle ABC with legs AB , BC and hypotenuse AC
using Pythagoras' identity in right triangle ABC
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
AB² + BC² = AC² ( substitute values )
x² + (x + 2)² = (x + 4)² ← expand factors using FOIL
x² + x² + 4x + 4 = x² + 8x + 16
2x² + 4x + 4 = x² + 8x + 16 ( subtract x² + 8x + 16 from both sides )
x² - 4x - 12 = 0 ← in standard form
(x - 6)(x + 2) = 0 ← in factored form
equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 2 = 0 ⇒ x = - 2
however , x > 0 , then x = 6
El perímetro de un módulo de vigilancia en forma de pentagono regular es de 35 metro, si un trabajador se le encargo pintar uno de sus muros para lo cual cobrar por metro lineal ¿cuantos metros pintará?
Answer:El pintor debe pintar un muro de módulo de vigilancia, que es un pentágono regular, por tanto, procedemos a buscar cuántos metros debe pintar: P = 5·L 35 m = 5·L L = 35 m / 5 L = 7 m En consecuencia, al pintar un muro, el trabajador pintará 7 m.
Step-by-step explanation:
El trabajador pintará 7 metros de muro, ya que esa es la longitud de cada lado del pentágono regular cuyo perímetro es de 35 metros.
Explanation:Un pentágono regular es una figura con cinco lados iguales. Si su perímetro total es de 35 metros, entonces cada lado del pentágono mide 35 metros dividido entre 5, que resulta igual a 7 metros. Entonces, si el trabajador debe pintar uno de los muros del pentágono regular, la cantidad de metros lineales a pintar será igual a la longitud de uno de sus lados. Por lo tanto, el trabajador pintará 7 metros de muro.
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what comes next in the sequence
7,10,19,34
Based on the pattern we identified, the next term in the sequence would be 55.
The sequence should be 7, 10, 19, 34, 55
To identify the pattern and determine what comes next in the given sequence (7, 10, 19, 34), we need to examine the relationship between the terms and look for a consistent pattern.
If we calculate the differences between consecutive terms, we get:
10 - 7 = 3
19 - 10 = 9
34 - 19 = 15
By examining the differences, we notice that they are increasing by 6 each time.
This suggests that the sequence might be formed by adding an increasing number to each term.
Let's calculate the next difference:
15 + 6 = 21
Now, let's add this difference to the last term of the sequence:
34 + 21 = 55
Therefore, based on the pattern we identified, the next term in the sequence would be 55.
To summarize:
7, 10, 19, 34, 55
It's important to note that without further context or information, this pattern is just one of the possibilities and may not be the only correct answer.
Additional terms or a different pattern may emerge if more information is provided.
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For two invertible n by n matrices A, B,
where rank(A)=rank(B)=n,
is the following always true?
"rank(AB) = n"
If so,
I wonder how we can prove it.
If not,
I'd appreciate you if you show me a counterexample.
Thank you in advance.
The statement "rank(AB) = n" is not always true for invertible n by n matrices A and B with rank(A) = rank(B) = n.
Counterexample:
Consider the following counterexample:
[tex]A = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}\\B = \begin{bmatrix} 1 & 0 \ 0 & 0 \end{bmatrix}[/tex]
Both matrices A and B are invertible, as they are both identity matrices. However, when we multiply them together, we get:
[tex]AB = \begin{bmatrix} 1 & 0 \ 0 & 0 \end{bmatrix}[/tex]
The rank of AB is 1, not n. In this case, n = 2, but rank(AB) = 1. Therefore, the statement "rank(AB) = n" is not always true for all invertible n by n matrices A and B with rank(A) = rank(B) = n.
In general, the rank of the product AB is less than or equal to the minimum of the ranks of A and B. So, in order for rank(AB) to be equal to n, both A and B need to have rank n individually, but that does not guarantee the rank of their product to be n as well.
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WILL GIVE 100 points A deli wraps its cylindrical containers of hot food items with plastic wrap. The containers have a diameter of 3.5 inches and a height of 4 inches. What is the minimum amount of plastic wrap needed to completely wrap 6 containers? Round your answer to the nearest tenth and approximate using π = 3.14.
44.0 in2
63.2 in2
379.2 in2
505.5 in2
Answer:
379.2 in^2
Step-by-step explanation:
Each cylinder's side area is pi *d * h = 43.98 in^2
you need six : =263.89 in^2
each ned of the cylinder area = pi r^2 = 9.621 in^2
and you have 12 ends for 115.45 in^2
For total : 379.3 in^2 (slight difference due to the value of pi used and rounding)
100 POINTS Use the drawing tool(s) to form the correct answer on the provided graph.
Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry for the function below.
The x-intercepts, y-intercept, vertex, and axis of symmetry for the given function g(x) = x² + 4x + 3 have been plotted on the graph below.
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).
Since the leading coefficient (value of a) in the given quadratic function g(x) = x² + 4x + 3 is positive 1, we can logically deduce that the parabola would open upward and the x-intercept (roots) is given by the ordered pair (-3, 0) and (-1, 0).
In conclusion, the vertex is given by the ordered pair (-2, -1) and the minimum value is -1.
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Answer:
x-intercepts = (-3, 0) and (-1, 0)
y-intercept = (0, 3)
Vertex = (-2, -1)
Axis of symmetry: x = -2
Step-by-step explanation:
Given quadratic function:
[tex]g(x) = x^2 + 4x + 3[/tex]
[tex]\hrulefill[/tex]
x-interceptsTo find the x-intercepts of the given function g(x), set g(x) equal to zero and solve for x.
Set g(x) = 0:
[tex]x^2 + 4x + 3 = 0[/tex]
Factor the quadratic equation:
[tex]x^2+x+3x+3=0[/tex]
[tex]x(x+1)+3(x+1)=0[/tex]
[tex](x + 3)(x + 1) = 0[/tex]
Set each factor equal to zero and solve for x:
[tex]x + 3 = 0 \implies x = -3[/tex]
[tex]x + 1 = 0 \implies x = -1[/tex]
Therefore, the x-intercepts are at (-3, 0) and (-1, 0).
[tex]\hrulefill[/tex]
y-interceptTo find the y-intercept of g(x), substitute x = 0 and solve for y.
[tex]\begin{aligned}x=0 \implies y&= (0)^2 + 4(0) + 3\\y& = 0 + 0 + 3 \\y&= 3\end{aligned}[/tex]
Therefore, the y-intercept is at (0, 3).
[tex]\hrulefill[/tex]
VertexThe x-value of the vertex of a parabola in the form y = ax² + bx + c is x = -b/2a.
For the function g(x), a = 1, and b = 4.
Therefore, the x-coordinate of the vertex is:
[tex]\textsf{$x$-coordinate of vertex} = \dfrac{-b}{2a} = \dfrac{-4}{2(1)} = -2[/tex]
To find the y-coordinate of the vertex, substitute x = -2 into function g(x):
[tex]\begin{aligned}x=-2 \implies y &= (-2)^2 + 4(-2) + 3\\y& = 4-8 + 3 \\y&= -1\end{aligned}[/tex]
Therefore, the vertex is at (-2, -1).
[tex]\hrulefill[/tex]
Axis of symmetryThe axis of symmetry of a vertical parabola is the x-coordinate of its vertex.
As the x-coordinate of the vertex is -2, the axis of symmetry is x = -2.
[tex]\hrulefill[/tex]
SummaryThe x-intercepts are at (-3, 0) and (-1, 0).The y-intercept is at (0, 3).The vertex is at (-2, -1).The axis of symmetry is x = -2.A 18-foot ladder leaning against a building forms an 22angle with the side of the building How far is the base of the ladder from the base of the building?
Answer:
Using the sine function, we have:
sin(angle) = opposite / hypotenuse
sin(22 degrees) = opposite / 18 feet
We can rearrange this equation to solve for the opposite side (height of the building):
opposite = sin(22 degrees) * 18 feet
Calculating this:
opposite ≈ 6.24 feet
Therefore, the base of the ladder from the base of the building is approximately 6.24 feet.
6.) Find the area of the circle shown.
a.
16 m²
b.
25 m²
c.
d.
50 m²
101 m²
7.) Find the perimeter of the circle shown in the previous question.
a. 12.5 m
b.
25 m
C. 50 m
d. 101 m
8.) Find the area of the figure. Assume right angles
a. 122u²
b. 126u²
c. 114u²
d. 156u²
9.) Find the geometric mean between 8 and 25.
a. 33
b. 17
c. 10√2
d. 20
13
10.) The perimeter of an equilateral triangle is 18. Find the measure of the altitude.
a. 3
b. 6
с 3V2
d. 3√3
Solution
verified
Verified by Toppr
The circumference of circle is 2πr=176
2×
7
22
×r=176
r=176×
22
7
2
1
r=7×4=28cm
Area of circle is πr
2
=
7
22
×28×28=88×28=2464cm
2
Jessica and Barry squeezed oranges for juice. Jessica squeezed 23
5
cups of juice. Barry made 1
4
cup less than Jessica. Barry estimated that Jessica squeezed about 21
2
cups of juice.
Which is the best estimate for the amount of juice Barry made?
The best estimate for the amount of juice Barry made is 235 cups.
In this question, Jessica and Barry squeezed oranges for juice. Jessica squeezed 235 cups of juice. Barry made 14 cups less than Jessica. Barry estimated that Jessica squeezed about 212 cups of juice. We need to find the best estimate for the amount of juice Barry made.
Let's begin by finding the amount of juice Barry actually made. Barry made 14 cups less than Jessica, which means he made: 235 - 14 = 221 cups of juice.
Now, let's compare this to Barry's estimate. Barry estimated that Jessica squeezed about 212 cups of juice. Since Jessica actually squeezed 235 cups of juice, her estimate was too low by:235 - 212 = 23 cups.
So, we can apply this error to Barry's estimate to get a better estimate for the amount of juice he made. If Barry's estimate was 212 cups, and he underestimated by 23 cups, then he actually made:212 + 23 = 235 cups of juice. Therefore, the best estimate for the amount of juice Barry made is 235 cups.
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F(x)=square root of 9-kx^2/k show your work
Sure! Here’s the solution:
F(x)=k9−kx2
First, let’s square both sides to get rid of the square root:
F(x)2=k9−kx2
Now, let’s multiply both sides by k to isolate the term with x^2:
kF(x)2=9−kx2
Next, let’s move all terms to one side of the equation:
kF(x)2+kx2=9
Finally, let’s factor out x^2:
x2(k+kF(x)2)=9
And solve for x^2:
x2=k+kF(x)29
Answer:
√((9 - kx^2) / k)Step-by-step explanation:
To show the work for evaluating the function f(x) = √(9 - kx^2) / k, we can follow these steps:
Step 1: Simplify the expression under the square root:9 - kx^2
Step 2: Divide the expression by k:(9 - kx^2) / k
Step 3: Take the square root of the expression:√((9 - kx^2) / k)
Note: It is important to consider any domain restrictions or assumptions about the values of k and x that would make the expression valid. For example, if k is negative, the expression would have an imaginary result.A total of 27 students are in your class. There are nine more males than females.
How many females are in your class?
Fill in the blanks below in order to justify whether or not the mapping shown represents a function.
The mapping shown does not represents a function
Determining if the mapping is a functionFrom the question, we have the following parameters that can be used in our computation:
The mapping
From the mapping, we have
(1, 7), (8, 3), (8, -1) and (3, 0)
The above ordered pair is not a function
This is so because the input value 8 have different output values 3 and -1
i.e. it would not pass the vertical line test when represented on a graph
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what is critical number
Answer:
A critical number can have different meanings depending on the context. In mathematics, a critical number is a value of x where the derivative of a function is zero or undefined. It helps to find the maximum and minimum of a function. In business, a critical number is a metric that represents a weakness or vulnerability that needs to be addressed and corrected to improve the performance and security of the company
Step-by-step explanation:
The graph of line I is shown below. Which of the following represents the slope of a line parallel to line P
Answer:
C) -1/3
Step-by-step explanation:
Slope=rise/run
Slope=-1/3
determine the surface area and volume
Answer:
surface area=214cm2, volume=183 cm3
Step-by-step explanation:
slanted height=√5^2+7^2 (Pythagoras theorem)
= √74
area of bottom part=π(5)^2
=25π
area of top cone part=π(5)(√74)
surface area of cone=25π+π(5)(√74)
=214 cm2(to 3 s.f.)
volume of cone=1/3π(5)^2×7
=183 cm3(to 3 s.f.)
10 points for this question
OThe presence of identical fossil plants in both Antarctica and Australia, within the same rock formations, supports the hypothesis of a supercontinent and the process of plate tectonics by providing evidence of past land connections and the subsequent separation of continents due to tectonic activity.
How to explain the informationThe presence of identical fossil plant species in rock formations of both Antarctica and Australia suggests that these two regions were once connected geographically. The similarity in the fossil record indicates that the plants existed in a shared ecosystem or environment at some point in the past.
The geological formations in which the fossil plants are found can provide further evidence. If the rock layers containing the fossils can be matched across Antarctica and Australia, it suggests that these regions were once part of the same landmass. This correlation supports the idea of a supercontinent.
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Please answer ASAP I will brainlist
Answer:
(a) The graph is entirely above the x-axis and rises from left to right, more steeply than the graph of y = 5^x.
(b) The second coordinate of the point with first coordinate 0 is 2.
The second coordinate of the point with first coordinate 1 is 10.
Please answer ASAP I will brainlist
Answer:
(a) The graph is an exponential growth curve.
(b) f(0) = 2, f(1) = 10
(c) The graph is entirely above the x-axis and increases from left to right, more steeply than the graph of y=5ˣ.
Step-by-step explanation:
Given function:
[tex]k(x)=2(5)^x[/tex]
[tex]\hrulefill[/tex]
Part (a)The graph is an exponential growth curve.
The curve begins in quadrant II, crosses the y-axis at (0, 2) into quadrant I, and increases rapidly as x increases.
In general, an exponential growth function is in the form:
[tex]\boxed{y = ab^x}[/tex]
where:
a is the y-intercept.b is the base.In this case, the y-intercept is 2 and the base is 5.
As the value of a is positive, and the value of b is greater than 1, it indicates exponential growth.
[tex]\hrulefill[/tex]
Part (b)The term "second coordinates" refers to the y-values of the points on a graph.
To find the second coordinates of the points with first coordinates 0 and 1, substitute x = 0 and x = 1 into the function and solve.
[tex]\begin{aligned}k(0)&=2(5)^{0}\\&=2(1)\\&=2\end{aligned}[/tex]
[tex]\begin{aligned}k(1)&=2(5)^{1}\\&=2(5)\\&=10\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Part (c)The graph is entirely above the x-axis and increases from left to right, more steeply than the graph of y=5ˣ.
As 2(5)ˣ > 0, the graph is entirely above the x-axis.
The end behaviour of the function is:
As x → -∞, k(x) → 0.As x → ∞, k(x) → ∞.Therefore, the graph increases from left to right.
In y = 2(5)ˣ, the base is 5, but it is multiplied by 2. This means that for every unit increase in x, the corresponding y-value is doubled compared to the graph of y = 5ˣ. Therefore, the multiplication by 2 makes the graph of y = 2(5)ˣ steeper than the graph of y = 5ˣ.
The graph is completely on the x-axis; It then increases from left to right. it is less steep that y = 5ˣ
The values are (0, 2) and (1, 10)
How to determine the shape of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2(5ˣ)
The above function is an exponential growth curve
This means that
The graph is completely on the x-axisIt then increases from left to rightit is less steep that y = 5ˣCalculating the values of the functionHere, we have
f(x) = 2(5ˣ)
This gives
f(0) = 2(5⁰)
f(0) = 2
f(1) = 2(5¹)
f(1) = 10
So, the values are (0, 2) and (1, 10)
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Antiderivative with the equation
The antiderivative of the function is f(x) = 2x + 5x³ + 2x⁶ - 9.
Find an antiderivative of f(x)To find an antiderivative of f(x), we can integrate each term of f'(x) individually.
Given:
f'(x) = 2 + 15x² + 12x⁵
To integrate 2, we get:
∫2 dx = 2x + C₁, where C₁ is the constant of integration.
To integrate 15x², we get:
∫15x² dx = 5x³ + C₂, where C₂ is another constant of integration.
To integrate 12x⁵, we get:
∫12x⁵ dx = 2x⁶ + C₃, where C₃ is another constant of integration.
Putting it all together, the antiderivative of f(x) is:
f(x) = 2x + 5x³ + 2x⁶ + C,
where C = C₁ + C₂ + C₃ represents the constant of integration.
To find the specific value of C, we are given that f(1) = 0. Substituting x = 1 into the antiderivative equation:
0 = 2(1) + 5(1)³ + 2(1)⁶ + C,
0 = 2 + 5 + 2 + C,
0 = 9 + C.
Therefore, C = -9.
The final expression for f(x) is:
f(x) = 2x + 5x³ + 2x⁶ - 9.
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PLEASEEEE HELP I GIVE YOU 100 POINTS
The missing dimensions from the given expression should be completed with the following:
(81.) A) 2
(82.) AD) x
(83.) E) 12
The expression as a product should be written as: DE) 2(x + 12).
What is a factored form?In Mathematics and Geometry, a factored form simply refers to a type of quadratic expression that is typically written as the product of two (2) linear factors and a constant.
In this scenario and exercise, we would complete the table above by showing the factored form and expanded form of each of the given expressions as follows;
x 12
2 2x 24
Note: 2x/2 = x.
24/2 = 12.
Next, we would write the expression 2x + 24 as a product as follows;
(2x + 24) = 2(x + 12).
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